On January 12, 2010, a magnitude 7.0 earthquake struck Haiti causing significant damage which affected approximately 3 million citizens. In the wake of the disaster, aid groups were working to locate displaced persons and provide them with food and water. However, due to the large scale destruction of infrastructure over a wide area additional assistance was needed to locate people quickly.
Little is left of a neighborhood on a hillside near downtown Port-au-Prince on Jan. 15. More than a million people were displaced by the quake. (David Gilkey/NPR)
Displaced persons were known to be making make-shift shelters out of blue tarps. High resolution geo-refereneced images were captured by aircraft of the destroyed areas. The data generated by the image collection was too large for aid workers to process in time to supply aid. Therefore, a team from the Rochester Institute of Technology used data-mining algorithms to analyze the images and identify blue tarps. The goal was to effectively locate displaced persons and communicate their location to rescue workers so they could get resources to people who needed it in time.
Sample image of a geo-referenced image used for the analysis
As the final project for SYS 6018 - Data Mining, we were assigned to build models from the different techniques we learned in the course to, as accurately as possible, and in as timely a manner as possible, locate as many of the displaced persons identified in the imagery data so that they could be provided food and water before their situations became unsurvivable. The data made available to students consisted of a csv of red, green, blue pixel values and a class indicator which indicated if a pixel was representative of a blue tarp or something else like vegetation. A final hold-out data set presented in the format of multiple text files was provided as well.
The US Government spent $1.5B on Haiti disaster relief by the end of 2010. For this project, we will assume that 5 million dollars were allocated to our team to deliver supplies to displaced individuals in the immediate aftermath. Our team has been assigned an area where 8,000 displaced people are expected to be. Anything less than a 85% delivery success rate will be considered a disaster relief failure. 85% of 8,000 people is 6,800.
| Budget | $5,000,000 |
| Cost per Delivery (True Positive) | |
| Cost per Mis-Delivery (False Positive) |
The data provided for analysis was generated from overhead images and stored as a three channel output. Each pixel also had a classifier label indicating whether it was a blue tarp or something else like vegetation or soil. The channels represented the red, green, and blue values for pixels within images. RGB color model is referred to as an additive model. The integer value for the red, green, and blue channels are combined to represent a color. Typically, the component values are stored as an 8 bit integer ranging from 0 to 255.
df <- tibble(read.csv("HaitiPixels.csv")) #read in df
"Check for NA values"
anyNA(df) #check for NA values
"Summary of Data"
summary(df) #quick look at data
df$Class <- factor(df$Class) #make Class a factor variable.
#> [1] "Check for NA values"
#> [1] FALSE
#> [1] "Summary of Data"
#> Class Red Green Blue
#> Length:63241 Min. : 48 Min. : 48.0 Min. : 44.0
#> Class :character 1st Qu.: 80 1st Qu.: 78.0 1st Qu.: 63.0
#> Mode :character Median :163 Median :148.0 Median :123.0
#> Mean :163 Mean :153.7 Mean :125.1
#> 3rd Qu.:255 3rd Qu.:226.0 3rd Qu.:181.0
#> Max. :255 Max. :255.0 Max. :255.0
#Reference [1]
# The palette with grey:
cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
# To use for fills, add
#scale_fill_manual(values=cbPalette)
ggpairs(df[,2:4], lower.panel = NULL, upper = list(continuous = wrap("cor", size = 3)), aes(color=df$Class))# + scale_fill_manual(values=cbPalette)
#view scatter and correlations
attach(df) #attach df variables
fig <- plot_ly(df, x=~Red, y=~Green, z=~Blue, color=~Class) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig <- fig %>% add_markers()
fig <- fig %>% layout(scene=list(xaxis=list(title="Red"),
yaxis = list(title = 'Green'),
zaxis = list(title = 'Blue')))
fig
!!!!!!!!!! IF I HAVE TIME MAKE A SELECTOR TO CHOOSE COLOR SCHEME FOR NOT COLOR BLIND OR DIFFERENT KINDS OF COLOR BLIND https://socviz.co/refineplots.html
Initial inspection of the data frame indicated no missing values. The data provided is sufficiently cleaned only one further adjustment to the data frame is needed. Since our main interest is to predict whether a pixel represents a blue tarp or not a blue tarp, the Class column of the data frame needs to be converted into a binary indicator for blue tarp or not blue tarp. This is done in the next section.
The data was visualized with the ggpairs function. For a pair of variables chosen from the data frame, Ggpairs generates a scatterplot, displays a Pearson correlation, and, on the diagonal, shows a variable distribution. The plots were also color-coded by class. The class label describes what kind of object a pixel is associated with. In our data frame there were the following classes: Blue Tarp, Rooftop, Soil, Various Non-tarp, and Vegetation. The 2D representation of the data only gives us a partial insight into the behavior and relationships of the predictors. Since three channels are used to generate a color, plotting the data in 3D to investigate trends and behavior between classes will be more meaningful.
The 3D scatter plot shows a significant amount of overlap between the different classes. It is worth noting that it is possible to see some separation between the classes.
df <- cbind(mutate(df, "Blue_Tarp_or_Not"=ifelse(Class != "Blue Tarp", 0, 1))) #add binary column indicating whether the Class variable is "Blue Tarp" or not
attach(df)
df$Blue_Tarp_or_Not <- factor(Blue_Tarp_or_Not, labels = c("NBT", "BT"))#, levels =c(0,1), labels = c("NBT", "BT")) #ensure new column is a factor
"First Six Rows of Data Frame"
head(df)
df_factor <- df[, -1]
"Last Six Rows of Data Frame"
tail(df_factor)
attach(df_factor)
#> [1] "First Six Rows of Data Frame"
#> Class Red Green Blue Blue_Tarp_or_Not
#> 1 Vegetation 64 67 50 NBT
#> 2 Vegetation 64 67 50 NBT
#> 3 Vegetation 64 66 49 NBT
#> 4 Vegetation 75 82 53 NBT
#> 5 Vegetation 74 82 54 NBT
#> 6 Vegetation 72 76 52 NBT
#> [1] "Last Six Rows of Data Frame"
#> Red Green Blue Blue_Tarp_or_Not
#> 63236 136 145 150 BT
#> 63237 138 146 150 BT
#> 63238 134 141 152 BT
#> 63239 136 143 151 BT
#> 63240 132 139 149 BT
#> 63241 133 141 153 BT
fig1 <- plot_ly(df_factor, x=~Red, y=~Green, z=~Blue, color=~Blue_Tarp_or_Not) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig1 <- fig1 %>% add_markers()
fig1 <- fig1 %>% layout(scene=list(xaxis=list(title="Red"),
yaxis = list(title = 'Green'),
zaxis = list(title = 'Blue')))
fig1
After the class label is converted into a binary classifier, it is easier to see separation between the data points for blue tarps and not blue tarps.
set.seed(4)
#In order to make run times faster when tuning parameters subset data with 20%
trainIndex <- createDataPartition(df_factor$Blue_Tarp_or_Not, p=0.2,
list=FALSE,
times=1)
df_subset <- df_factor[trainIndex,]
Fit a Logistic Regression Model !!!Need to turn on the fold result saving …
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
glm.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,
method="glm",
family="binomial",
trControl= fitControl)
glm.fit
"Summary"
summary(glm.fit)
#> Generalized Linear Model
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> No pre-processing
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9956522 0.9268774
#>
#> [1] "Summary"
#>
#> Call:
#> NULL
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -3.3875 -0.0135 -0.0005 0.0000 3.1857
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.06785 0.48917 2.183 0.029 *
#> Red -0.34277 0.04015 -8.538 < 2e-16 ***
#> Green -0.22358 0.03578 -6.249 4.13e-10 ***
#> Blue 0.55714 0.04609 12.089 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 3584.46 on 12648 degrees of freedom
#> Residual deviance: 317.48 on 12645 degrees of freedom
#> AIC: 325.48
#>
#> Number of Fisher Scoring iterations: 12
Test model performance on Train data to select threshold values…
#pass
glm.prob <- predict(glm.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
glm_roc <- roc(df_subset $Blue_Tarp_or_Not, glm.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="Log. Reg. ROC Curve")
roc.info_glm <- roc(df_subset$Blue_Tarp_or_Not, glm.prob[,2], legacy.axes=TRUE)
roc.glm.df <- data.frame(tpp=roc.info_glm$sensitivities*100, fpp=(1-roc.info_glm$specificities)*100, thresholds=roc.info_glm$thresholds)
#roc.glm.df[roc.glm.df>98.5 & roc.glm.df < 99,]
glm.thresholds <- data.matrix(roc.glm.df$thresholds)
fig2 <- plot_ly(roc.glm.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig2 <- fig2 %>% add_markers()
fig2 <- fig2 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig2
lr.thresh <- 0.5
glm.pred_thresh <- factor(ifelse(glm.prob[,2]>lr.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.glm_thresh <- confusionMatrix(factor(glm.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.glm_thresh
acc_LR <- cm.glm_thresh[["overall"]][["Accuracy"]]*100
auc_LR <- glm_roc[["auc"]]
thresh_LR <- lr.thresh
sens_LR <- cm.glm_thresh[["byClass"]][["Sensitivity"]]*100
spec_LR <- cm.glm_thresh[["byClass"]][["Specificity"]]*100
FDR_LR <- ((cm.glm_thresh[["table"]][2,1])/(cm.glm_thresh[["table"]][2,1]+cm.glm_thresh[["table"]][2,2]))*100
prec_LR <- cm.glm_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12234 46
#> BT 10 359
#>
#> Accuracy : 0.9956
#> 95% CI : (0.9943, 0.9967)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2.2e-16
#>
#> Kappa : 0.9254
#>
#> Mcnemar's Test P-Value : 2.91e-06
#>
#> Sensitivity : 0.88642
#> Specificity : 0.99918
#> Pos Pred Value : 0.97290
#> Neg Pred Value : 0.99625
#> Prevalence : 0.03202
#> Detection Rate : 0.02838
#> Detection Prevalence : 0.02917
#> Balanced Accuracy : 0.94280
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
glm.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
glm.sd <- sd(glm.fit[["resample"]][["Accuracy"]]*100)
#plot(glm.fit[["resample"]][["Accuracy"]], main="Accuracy per Fold", xlab= "Fold Number", ylab="Accuracy")
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9968379 0.9495865 none Fold01
#> 2 0.9976266 0.9598169 none Fold02
#> 3 0.9944664 0.9038284 none Fold03
#> 4 0.9944708 0.9085430 none Fold04
#> 5 0.9952607 0.9206386 none Fold05
#> 6 0.9960474 0.9330355 none Fold06
#> 7 0.9944664 0.9085407 none Fold07
#> 8 0.9952532 0.9164905 none Fold08
#> 9 0.9968354 0.9457418 none Fold09
#> 10 0.9952569 0.9225526 none Fold10
The average accuracy across ten folds is 99.56 with a standard deviation of 0.113.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
lda.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="lda",
verbose= FALSE,
trControl= fitControl)
lda.fit
"Summary"
summary(lda.fit)
#> Linear Discriminant Analysis
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9825284 0.737388
#>
#> [1] "Summary"
#> Length Class Mode
#> prior 2 -none- numeric
#> counts 2 -none- numeric
#> means 6 -none- numeric
#> scaling 3 -none- numeric
#> lev 2 -none- character
#> svd 1 -none- numeric
#> N 1 -none- numeric
#> call 4 -none- call
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 1 -none- list
#pass
lda.prob <- predict(lda.fit, newdata=df_subset, type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
lda_roc <- roc(df_subset$Blue_Tarp_or_Not, lda.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="LDA ROC Curve")
roc.info_lda <- roc(df_subset $Blue_Tarp_or_Not, lda.prob[,2], legacy.axes=TRUE)
roc.lda.df <- data.frame(tpp=roc.info_lda$sensitivities*100, fpp=(1-roc.info_lda$specificities)*100, thresholds=roc.info_lda$thresholds)
#roc.lda.df[roc.lda.df>91.5 & roc.lda.df < 91.6,]
fig3 <- plot_ly(roc.lda.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig3 <- fig3 %>% add_markers()
fig3 <- fig3 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig3
lda.thresh <- 0.5
lda.pred_thresh <- factor(ifelse(lda.prob[,2]>lda.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.lda_thresh <- confusionMatrix(factor(lda.pred_thresh),df_subset$Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.lda_thresh
acc_lda <- cm.lda_thresh[["overall"]][["Accuracy"]]*100
auc_lda <- lda_roc[["auc"]]
thresh_lda <- lr.thresh
sens_lda <- cm.lda_thresh[["byClass"]][["Sensitivity"]]*100
spec_lda <- cm.lda_thresh[["byClass"]][["Specificity"]]*100
FDR_lda <- ((cm.lda_thresh[["table"]][2,1])/(cm.lda_thresh[["table"]][2,1]+cm.lda_thresh[["table"]][2,2]))*100
prec_lda <- cm.lda_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12108 81
#> BT 136 324
#>
#> Accuracy : 0.9828
#> 95% CI : (0.9804, 0.985)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2.2e-16
#>
#> Kappa : 0.7403
#>
#> Mcnemar's Test P-Value : 0.0002466
#>
#> Sensitivity : 0.80000
#> Specificity : 0.98889
#> Pos Pred Value : 0.70435
#> Neg Pred Value : 0.99335
#> Prevalence : 0.03202
#> Detection Rate : 0.02561
#> Detection Prevalence : 0.03637
#> Balanced Accuracy : 0.89445
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
lda.fit$resample
lda.sd <- sd(lda.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9770751 0.6831354 none Fold01
#> 2 0.9849684 0.7835304 none Fold02
#> 3 0.9802372 0.7089679 none Fold03
#> 4 0.9834123 0.7384143 none Fold04
#> 5 0.9857820 0.7731409 none Fold05
#> 6 0.9826087 0.7519564 none Fold06
#> 7 0.9794466 0.7005426 none Fold07
#> 8 0.9833861 0.7321602 none Fold08
#> 9 0.9849684 0.7576687 none Fold09
#> 10 0.9833992 0.7443633 none Fold10
The average accuracy across ten folds is 98.28 with a standard deviation of 0.277.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
qda.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="qda",
verbose= FALSE,
trControl= fitControl)
qda.fit
"Summary"
summary(qda.fit)
#> Quadratic Discriminant Analysis
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9946241 0.9060525
#>
#> [1] "Summary"
#> Length Class Mode
#> prior 2 -none- numeric
#> counts 2 -none- numeric
#> means 6 -none- numeric
#> scaling 18 -none- numeric
#> ldet 2 -none- numeric
#> lev 2 -none- character
#> N 1 -none- numeric
#> call 4 -none- call
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 1 -none- list
#pass
qda.prob <- predict(qda.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
qda_roc <- roc(df_subset $Blue_Tarp_or_Not, qda.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="QDA ROC Curve")
roc.info_qda <- roc(df_subset$Blue_Tarp_or_Not, qda.prob[,2], legacy.axes=TRUE)
roc.qda.df <- data.frame(tpp=roc.info_qda$sensitivities*100, fpp=(1-roc.info_qda$specificities)*100, thresholds=roc.info_qda$thresholds)
#roc.qda.df[roc.qda.df>98 & roc.qda.df < 99,]
fig4 <- plot_ly(roc.qda.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig4 <- fig4 %>% add_markers()
fig4 <- fig4 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig4
qda.thresh <- 0.5
qda.pred_thresh <- factor(ifelse(qda.prob[,2]>qda.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.qda_thresh <- confusionMatrix(factor(qda.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.qda_thresh
acc_qda <- cm.qda_thresh[["overall"]][["Accuracy"]]*100
auc_qda <- qda_roc[["auc"]]
thresh_qda <- lr.thresh
sens_qda <- cm.qda_thresh[["byClass"]][["Sensitivity"]]*100
spec_qda <- cm.qda_thresh[["byClass"]][["Specificity"]]*100
FDR_qda <- ((cm.qda_thresh[["table"]][2,1])/(cm.qda_thresh[["table"]][2,1]+cm.qda_thresh[["table"]][2,2]))*100
prec_qda <- cm.qda_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12241 65
#> BT 3 340
#>
#> Accuracy : 0.9946
#> 95% CI : (0.9932, 0.9958)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2.2e-16
#>
#> Kappa : 0.9063
#>
#> Mcnemar's Test P-Value : 1.389e-13
#>
#> Sensitivity : 0.83951
#> Specificity : 0.99975
#> Pos Pred Value : 0.99125
#> Neg Pred Value : 0.99472
#> Prevalence : 0.03202
#> Detection Rate : 0.02688
#> Detection Prevalence : 0.02712
#> Balanced Accuracy : 0.91963
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
qda.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
qda.sd <- sd(qda.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9968379 0.9470877 none Fold01
#> 2 0.9960443 0.9313043 none Fold02
#> 3 0.9936759 0.8886566 none Fold03
#> 4 0.9944708 0.9038432 none Fold04
#> 5 0.9944708 0.9038432 none Fold05
#> 6 0.9952569 0.9186234 none Fold06
#> 7 0.9944664 0.9038409 none Fold07
#> 8 0.9944620 0.9012853 none Fold08
#> 9 0.9936709 0.8856729 none Fold09
#> 10 0.9928854 0.8763669 none Fold10
The average accuracy across ten folds is 99.46 with a standard deviation of 0.117.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
knn.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="knn",
trControl= fitControl,
tuneLength=10
)
knn.fit
#> k-Nearest Neighbors
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> k Accuracy Kappa
#> 5 0.9974702 0.9597379
#> 7 0.9970750 0.9531862
#> 9 0.9966004 0.9448613
#> 11 0.9962843 0.9398857
#> 13 0.9957310 0.9302483
#> 15 0.9958104 0.9316068
#> 17 0.9956522 0.9287919
#> 19 0.9955731 0.9271888
#> 21 0.9956521 0.9282576
#> 23 0.9954941 0.9251812
#>
#> Accuracy was used to select the optimal model using the largest value.
#> The final value used for the model was k = 5.
plot(knn.fit)
#pass
knn.prob <- predict(knn.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
knn_roc <- roc(df_subset $Blue_Tarp_or_Not, knn.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="KNN ROC Curve")
Not sure why there are only 10 values for this one…?
roc.info_knn <- roc(df_subset$Blue_Tarp_or_Not, knn.prob[,2], legacy.axes=TRUE)
roc.knn.df <- data.frame(tpp=roc.info_knn$sensitivities*100, fpp=(1-roc.info_knn$specificities)*100, thresholds=roc.info_knn$thresholds)
#roc.knn.df[roc.knn.df>99 & roc.knn.df < 100,]
#roc.knn.df
fig5 <- plot_ly(roc.knn.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig5 <- fig5 %>% add_markers()
fig5 <- fig5 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig5
knn.thresh <- 0.5
knn.pred_thresh <- factor(ifelse(knn.prob[,2]>knn.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.knn_thresh <- confusionMatrix(factor(knn.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.knn_thresh
acc_knn <- cm.knn_thresh[["overall"]][["Accuracy"]]*100
auc_knn <- knn_roc[["auc"]]
thresh_knn <- lr.thresh
sens_knn <- cm.knn_thresh[["byClass"]][["Sensitivity"]]*100
spec_knn <- cm.knn_thresh[["byClass"]][["Specificity"]]*100
FDR_knn <- ((cm.knn_thresh[["table"]][2,1])/(cm.knn_thresh[["table"]][2,1]+cm.knn_thresh[["table"]][2,2]))*100
prec_knn <- cm.knn_thresh[["byClass"]][["Precision"]]*100
k_knn <- knn.fit[["bestTune"]][["k"]]
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12228 8
#> BT 16 397
#>
#> Accuracy : 0.9981
#> 95% CI : (0.9972, 0.9988)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : <2e-16
#>
#> Kappa : 0.9697
#>
#> Mcnemar's Test P-Value : 0.153
#>
#> Sensitivity : 0.98025
#> Specificity : 0.99869
#> Pos Pred Value : 0.96126
#> Neg Pred Value : 0.99935
#> Prevalence : 0.03202
#> Detection Rate : 0.03139
#> Detection Prevalence : 0.03265
#> Balanced Accuracy : 0.98947
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
knn.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
knn.sd <- sd(knn.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa k Resample
#> 1 0.9976285 0.9626311 5 Fold01
#> 2 0.9968379 0.9495865 7 Fold01
#> 3 0.9968379 0.9495865 9 Fold01
#> 4 0.9960474 0.9377185 11 Fold01
#> 5 0.9960474 0.9377185 13 Fold01
#> 6 0.9960474 0.9377185 15 Fold01
#> 7 0.9960474 0.9377185 17 Fold01
#> 8 0.9968379 0.9495865 19 Fold01
#> 9 0.9968379 0.9495865 21 Fold01
#> 10 0.9960474 0.9362303 23 Fold01
#> 11 0.9984177 0.9741830 5 Fold02
#> 12 0.9984177 0.9741830 7 Fold02
#> 13 0.9976266 0.9608005 9 Fold02
#> 14 0.9976266 0.9608005 11 Fold02
#> 15 0.9976266 0.9608005 13 Fold02
#> 16 0.9976266 0.9608005 15 Fold02
#> 17 0.9968354 0.9483660 17 Fold02
#> 18 0.9968354 0.9483660 19 Fold02
#> 19 0.9976266 0.9608005 21 Fold02
#> 20 0.9976266 0.9608005 23 Fold02
#> 21 0.9968379 0.9495865 5 Fold03
#> 22 0.9968379 0.9483673 7 Fold03
#> 23 0.9976285 0.9608015 9 Fold03
#> 24 0.9976285 0.9608015 11 Fold03
#> 25 0.9968379 0.9470877 13 Fold03
#> 26 0.9968379 0.9470877 15 Fold03
#> 27 0.9968379 0.9470877 17 Fold03
#> 28 0.9968379 0.9470877 19 Fold03
#> 29 0.9968379 0.9470877 21 Fold03
#> 30 0.9968379 0.9470877 23 Fold03
#> 31 0.9976303 0.9634815 5 Fold04
#> 32 0.9968404 0.9507479 7 Fold04
#> 33 0.9960506 0.9377177 9 Fold04
#> 34 0.9936809 0.9014958 11 Fold04
#> 35 0.9936809 0.8991737 13 Fold04
#> 36 0.9936809 0.8991737 15 Fold04
#> 37 0.9936809 0.8991737 17 Fold04
#> 38 0.9936809 0.9014958 19 Fold04
#> 39 0.9944708 0.9128048 21 Fold04
#> 40 0.9944708 0.9107247 23 Fold04
#> 41 0.9976303 0.9626306 5 Fold05
#> 42 0.9968404 0.9495869 7 Fold05
#> 43 0.9968404 0.9495869 9 Fold05
#> 44 0.9976303 0.9626306 11 Fold05
#> 45 0.9968404 0.9495869 13 Fold05
#> 46 0.9952607 0.9225546 15 Fold05
#> 47 0.9952607 0.9225546 17 Fold05
#> 48 0.9952607 0.9225546 19 Fold05
#> 49 0.9952607 0.9225546 21 Fold05
#> 50 0.9952607 0.9225546 23 Fold05
#> 51 0.9984190 0.9741842 5 Fold06
#> 52 0.9976285 0.9608031 7 Fold06
#> 53 0.9976285 0.9608031 9 Fold06
#> 54 0.9976285 0.9608031 11 Fold06
#> 55 0.9976285 0.9608031 13 Fold06
#> 56 0.9976285 0.9608031 15 Fold06
#> 57 0.9976285 0.9608031 17 Fold06
#> 58 0.9968379 0.9470911 19 Fold06
#> 59 0.9968379 0.9470911 21 Fold06
#> 60 0.9960474 0.9330355 23 Fold06
#> 61 0.9960474 0.9404891 5 Fold07
#> 62 0.9960474 0.9404891 7 Fold07
#> 63 0.9960474 0.9404891 9 Fold07
#> 64 0.9960474 0.9391341 11 Fold07
#> 65 0.9952569 0.9261199 13 Fold07
#> 66 0.9944664 0.9128024 15 Fold07
#> 67 0.9936759 0.8991711 17 Fold07
#> 68 0.9936759 0.8967368 19 Fold07
#> 69 0.9928854 0.8824094 21 Fold07
#> 70 0.9928854 0.8824094 23 Fold07
#> 71 0.9992089 0.9869335 5 Fold08
#> 72 0.9976266 0.9608005 7 Fold08
#> 73 0.9952532 0.9186126 9 Fold08
#> 74 0.9952532 0.9186126 11 Fold08
#> 75 0.9944620 0.9038261 13 Fold08
#> 76 0.9960443 0.9313043 15 Fold08
#> 77 0.9952532 0.9164905 17 Fold08
#> 78 0.9952532 0.9164905 19 Fold08
#> 79 0.9952532 0.9164905 21 Fold08
#> 80 0.9952532 0.9164905 23 Fold08
#> 81 0.9952532 0.9206296 5 Fold09
#> 82 0.9960443 0.9346675 7 Fold09
#> 83 0.9952532 0.9206296 9 Fold09
#> 84 0.9952532 0.9206296 11 Fold09
#> 85 0.9952532 0.9206296 13 Fold09
#> 86 0.9968354 0.9470864 15 Fold09
#> 87 0.9976266 0.9598169 17 Fold09
#> 88 0.9968354 0.9457418 19 Fold09
#> 89 0.9960443 0.9330281 21 Fold09
#> 90 0.9968354 0.9457418 23 Fold09
#> 91 0.9976285 0.9626296 5 Fold10
#> 92 0.9976285 0.9626296 7 Fold10
#> 93 0.9968379 0.9495855 9 Fold10
#> 94 0.9960474 0.9362303 11 Fold10
#> 95 0.9936759 0.8967368 13 Fold10
#> 96 0.9936759 0.8967368 15 Fold10
#> 97 0.9936759 0.8967368 17 Fold10
#> 98 0.9936759 0.8967368 19 Fold10
#> 99 0.9944664 0.9107224 21 Fold10
#> 100 0.9936759 0.8967368 23 Fold10
The average accuracy across ten folds when k = 5 is 99.81 with a standard deviation of 0.144.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
rf.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="rf", #what is the difference between the different caret rf models??
trControl= fitControl,
tuneLength=3
)
rf.fit
#> note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .
#>
#> Random Forest
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> mtry Accuracy Kappa
#> 2 0.9968378 0.9488261
#> 3 0.9967588 0.9480005
#>
#> Accuracy was used to select the optimal model using the largest value.
#> The final value used for the model was mtry = 2.
plot(rf.fit)
#pass
RF.prob <- predict(rf.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
RF_roc <- roc(df_subset $Blue_Tarp_or_Not, RF.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="RF ROC Curve")
roc.info_rf <- roc(df_subset$Blue_Tarp_or_Not, RF.prob[,2], legacy.axes=TRUE)
roc.rf.df <- data.frame(tpp=roc.info_rf$sensitivities*100, fpp=(1-roc.info_rf$specificities)*100, thresholds=roc.info_rf$thresholds)
#roc.rf.df[roc.rf.df>99 & roc.rf.df < 100,]
#roc.rf.df
fig6 <- plot_ly(roc.rf.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig6 <- fig6 %>% add_markers()
fig6 <- fig6 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig6
RF.thresh <- 0.5
RF.pred_thresh <- factor(ifelse(RF.prob[,2]>RF.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.RF_thresh <- confusionMatrix(factor(RF.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.RF_thresh
acc_RF <- cm.RF_thresh[["overall"]][["Accuracy"]]*100
auc_RF <- RF_roc[["auc"]]
thresh_RF <- lr.thresh
sens_RF <- cm.RF_thresh[["byClass"]][["Sensitivity"]]*100
spec_RF <- cm.RF_thresh[["byClass"]][["Specificity"]]*100
FDR_RF <- ((cm.RF_thresh[["table"]][2,1])/(cm.RF_thresh[["table"]][2,1]+cm.RF_thresh[["table"]][2,2]))*100
prec_RF <- cm.RF_thresh[["byClass"]][["Precision"]]*100
mtry_best <- rf.fit[["bestTune"]][["mtry"]]
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12244 5
#> BT 0 400
#>
#> Accuracy : 0.9996
#> 95% CI : (0.9991, 0.9999)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2e-16
#>
#> Kappa : 0.9936
#>
#> Mcnemar's Test P-Value : 0.07364
#>
#> Sensitivity : 0.98765
#> Specificity : 1.00000
#> Pos Pred Value : 1.00000
#> Neg Pred Value : 0.99959
#> Prevalence : 0.03202
#> Detection Rate : 0.03162
#> Detection Prevalence : 0.03162
#> Balanced Accuracy : 0.99383
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
rf.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
rf.sd <- sd(rf.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa mtry Resample
#> 1 0.9976285 0.9617382 2 Fold01
#> 2 0.9960474 0.9377185 3 Fold01
#> 3 0.9992089 0.9869335 2 Fold02
#> 4 0.9992089 0.9869335 3 Fold02
#> 5 0.9960474 0.9346692 2 Fold03
#> 6 0.9968379 0.9483673 3 Fold03
#> 7 0.9976303 0.9634815 2 Fold04
#> 8 0.9976303 0.9634815 3 Fold04
#> 9 0.9960506 0.9346736 2 Fold05
#> 10 0.9952607 0.9206386 3 Fold05
#> 11 0.9984190 0.9741842 2 Fold06
#> 12 0.9984190 0.9741842 3 Fold06
#> 13 0.9960474 0.9404891 2 Fold07
#> 14 0.9960474 0.9404891 3 Fold07
#> 15 0.9960443 0.9313043 2 Fold08
#> 16 0.9968354 0.9457418 3 Fold08
#> 17 0.9960443 0.9346675 2 Fold09
#> 18 0.9960443 0.9346675 3 Fold09
#> 19 0.9952569 0.9261199 2 Fold10
#> 20 0.9952569 0.9277831 3 Fold10
The average accuracy across ten folds when mtry = 2 is 99.96 with a standard deviation of 0.127.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
svm.radial.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="svmRadial",
trControl= fitControl,
tuneLength=10
#tuneGrid = expand.grid(C=seq(0,10, length=10),
# sigma =seq(0,10, length=10))
)
svm.radial.fit
"Summary"
summary(svm.radial.fit)
#> Support Vector Machines with Radial Basis Function Kernel
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> C Accuracy Kappa
#> 0.25 0.9959682 0.9337974
#> 0.50 0.9962054 0.9377061
#> 1.00 0.9963636 0.9404512
#> 2.00 0.9970750 0.9522407
#> 4.00 0.9969959 0.9509235
#> 8.00 0.9969958 0.9507358
#> 16.00 0.9971538 0.9532823
#> 32.00 0.9969955 0.9503985
#> 64.00 0.9969957 0.9508143
#> 128.00 0.9968375 0.9480134
#>
#> Tuning parameter 'sigma' was held constant at a value of 9.406735
#> Accuracy was used to select the optimal model using the largest value.
#> The final values used for the model were sigma = 9.406735 and C = 16.
#> [1] "Summary"
#> Length Class Mode
#> 1 ksvm S4
plot(svm.radial.fit)
Both linear and poly SVM functions were considered. Radial SVM produced the highest accuracy values of the three methods. SVM radial was chosen for building the SVM model.
#pass
SVM.prob <- predict(svm.radial.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
SVM_roc <- roc(df_subset $Blue_Tarp_or_Not, SVM.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="SVM ROC Curve")
roc.info_svm <- roc(df_subset$Blue_Tarp_or_Not, SVM.prob[,2], legacy.axes=TRUE)
roc.svm.df <- data.frame(tpp=roc.info_svm$sensitivities*100, fpp=(1-roc.info_svm$specificities)*100, thresholds=roc.info_svm$thresholds)
#roc.svm.df[roc.svm.df>99 & roc.svm.df < 100,]
#roc.svm.df
fig7 <- plot_ly(roc.svm.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig7 <- fig7 %>% add_markers()
fig7 <- fig7 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig7
SVM.thresh <- 0.5
SVM.pred_thresh <- factor(ifelse(SVM.prob[,2]>SVM.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.SVM_thresh <- confusionMatrix(factor(SVM.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.SVM_thresh
acc_SVM <- cm.SVM_thresh[["overall"]][["Accuracy"]]*100
auc_SVM <- SVM_roc[["auc"]]
thresh_SVM <- lr.thresh
sens_SVM <- cm.SVM_thresh[["byClass"]][["Sensitivity"]]*100
spec_SVM <- cm.SVM_thresh[["byClass"]][["Specificity"]]*100
FDR_SVM <- ((cm.SVM_thresh[["table"]][2,1])/(cm.SVM_thresh[["table"]][2,1]+cm.SVM_thresh[["table"]][2,2]))*100
prec_SVM <- cm.SVM_thresh[["byClass"]][["Precision"]]*100
#sigma_best <- fill this in after best svm model chosen
#C_best <-
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12234 17
#> BT 10 388
#>
#> Accuracy : 0.9979
#> 95% CI : (0.9969, 0.9986)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : <2e-16
#>
#> Kappa : 0.9653
#>
#> Mcnemar's Test P-Value : 0.2482
#>
#> Sensitivity : 0.95802
#> Specificity : 0.99918
#> Pos Pred Value : 0.97487
#> Neg Pred Value : 0.99861
#> Prevalence : 0.03202
#> Detection Rate : 0.03067
#> Detection Prevalence : 0.03146
#> Balanced Accuracy : 0.97860
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
svm.radial.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
svm.sd <- sd(svm.radial.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa sigma C Resample
#> 1 0.9968379 0.9495865 9.406735 0.25 Fold01
#> 2 0.9976285 0.9617382 9.406735 0.50 Fold01
#> 3 0.9976285 0.9617382 9.406735 1.00 Fold01
#> 4 0.9984190 0.9747933 9.406735 2.00 Fold01
#> 5 0.9984190 0.9747933 9.406735 4.00 Fold01
#> 6 0.9984190 0.9747933 9.406735 8.00 Fold01
#> 7 0.9984190 0.9747933 9.406735 16.00 Fold01
#> 8 0.9984190 0.9747933 9.406735 32.00 Fold01
#> 9 0.9984190 0.9747933 9.406735 64.00 Fold01
#> 10 0.9992095 0.9872461 9.406735 128.00 Fold01
#> 11 0.9968354 0.9470864 9.406735 0.25 Fold02
#> 12 0.9976266 0.9608005 9.406735 0.50 Fold02
#> 13 0.9984177 0.9741830 9.406735 1.00 Fold02
#> 14 0.9984177 0.9741830 9.406735 2.00 Fold02
#> 15 0.9984177 0.9741830 9.406735 4.00 Fold02
#> 16 0.9984177 0.9741830 9.406735 8.00 Fold02
#> 17 0.9984177 0.9741830 9.406735 16.00 Fold02
#> 18 0.9984177 0.9741830 9.406735 32.00 Fold02
#> 19 0.9984177 0.9741830 9.406735 64.00 Fold02
#> 20 0.9984177 0.9741830 9.406735 128.00 Fold02
#> 21 0.9976285 0.9608015 9.406735 0.25 Fold03
#> 22 0.9976285 0.9608015 9.406735 0.50 Fold03
#> 23 0.9960474 0.9346692 9.406735 1.00 Fold03
#> 24 0.9960474 0.9330298 9.406735 2.00 Fold03
#> 25 0.9952569 0.9225510 9.406735 4.00 Fold03
#> 26 0.9944664 0.9085369 9.406735 8.00 Fold03
#> 27 0.9944664 0.9085369 9.406735 16.00 Fold03
#> 28 0.9944664 0.9085369 9.406735 32.00 Fold03
#> 29 0.9944664 0.9085369 9.406735 64.00 Fold03
#> 30 0.9936759 0.8941755 9.406735 128.00 Fold03
#> 31 0.9936809 0.8967395 9.406735 0.25 Fold04
#> 32 0.9944708 0.9107247 9.406735 0.50 Fold04
#> 33 0.9944708 0.9107247 9.406735 1.00 Fold04
#> 34 0.9960506 0.9377177 9.406735 2.00 Fold04
#> 35 0.9960506 0.9377177 9.406735 4.00 Fold04
#> 36 0.9960506 0.9377177 9.406735 8.00 Fold04
#> 37 0.9968404 0.9507479 9.406735 16.00 Fold04
#> 38 0.9976303 0.9634815 9.406735 32.00 Fold04
#> 39 0.9968404 0.9507479 9.406735 64.00 Fold04
#> 40 0.9968404 0.9507479 9.406735 128.00 Fold04
#> 41 0.9968404 0.9495869 9.406735 0.25 Fold05
#> 42 0.9952607 0.9225546 9.406735 0.50 Fold05
#> 43 0.9952607 0.9225546 9.406735 1.00 Fold05
#> 44 0.9960506 0.9362319 9.406735 2.00 Fold05
#> 45 0.9960506 0.9362319 9.406735 4.00 Fold05
#> 46 0.9968404 0.9483697 9.406735 8.00 Fold05
#> 47 0.9976303 0.9608041 9.406735 16.00 Fold05
#> 48 0.9976303 0.9608041 9.406735 32.00 Fold05
#> 49 0.9976303 0.9608041 9.406735 64.00 Fold05
#> 50 0.9976303 0.9608041 9.406735 128.00 Fold05
#> 51 0.9968379 0.9470911 9.406735 0.25 Fold06
#> 52 0.9976285 0.9608031 9.406735 0.50 Fold06
#> 53 0.9976285 0.9608031 9.406735 1.00 Fold06
#> 54 0.9984190 0.9741842 9.406735 2.00 Fold06
#> 55 0.9984190 0.9741842 9.406735 4.00 Fold06
#> 56 0.9984190 0.9741842 9.406735 8.00 Fold06
#> 57 0.9984190 0.9741842 9.406735 16.00 Fold06
#> 58 0.9976285 0.9608031 9.406735 32.00 Fold06
#> 59 0.9984190 0.9741842 9.406735 64.00 Fold06
#> 60 0.9984190 0.9741842 9.406735 128.00 Fold06
#> 61 0.9944664 0.9107224 9.406735 0.25 Fold07
#> 62 0.9952569 0.9243783 9.406735 0.50 Fold07
#> 63 0.9952569 0.9261199 9.406735 1.00 Fold07
#> 64 0.9968379 0.9507466 9.406735 2.00 Fold07
#> 65 0.9976285 0.9634805 9.406735 4.00 Fold07
#> 66 0.9976285 0.9634805 9.406735 8.00 Fold07
#> 67 0.9976285 0.9634805 9.406735 16.00 Fold07
#> 68 0.9976285 0.9634805 9.406735 32.00 Fold07
#> 69 0.9968379 0.9518554 9.406735 64.00 Fold07
#> 70 0.9968379 0.9518554 9.406735 128.00 Fold07
#> 71 0.9968354 0.9457418 9.406735 0.25 Fold08
#> 72 0.9960443 0.9313043 9.406735 0.50 Fold08
#> 73 0.9968354 0.9457418 9.406735 1.00 Fold08
#> 74 0.9984177 0.9735432 9.406735 2.00 Fold08
#> 75 0.9976266 0.9598169 9.406735 4.00 Fold08
#> 76 0.9976266 0.9598169 9.406735 8.00 Fold08
#> 77 0.9976266 0.9598169 9.406735 16.00 Fold08
#> 78 0.9976266 0.9598169 9.406735 32.00 Fold08
#> 79 0.9976266 0.9598169 9.406735 64.00 Fold08
#> 80 0.9968354 0.9470864 9.406735 128.00 Fold08
#> 81 0.9944620 0.9062394 9.406735 0.25 Fold09
#> 82 0.9944620 0.9062394 9.406735 0.50 Fold09
#> 83 0.9944620 0.9062394 9.406735 1.00 Fold09
#> 84 0.9944620 0.9062394 9.406735 2.00 Fold09
#> 85 0.9936709 0.8914835 9.406735 4.00 Fold09
#> 86 0.9936709 0.8914835 9.406735 8.00 Fold09
#> 87 0.9936709 0.8914835 9.406735 16.00 Fold09
#> 88 0.9928797 0.8763478 9.406735 32.00 Fold09
#> 89 0.9936709 0.8914835 9.406735 64.00 Fold09
#> 90 0.9936709 0.8914835 9.406735 128.00 Fold09
#> 91 0.9952569 0.9243783 9.406735 0.25 Fold10
#> 92 0.9960474 0.9377160 9.406735 0.50 Fold10
#> 93 0.9976285 0.9617382 9.406735 1.00 Fold10
#> 94 0.9976285 0.9617382 9.406735 2.00 Fold10
#> 95 0.9984190 0.9747928 9.406735 4.00 Fold10
#> 96 0.9984190 0.9747928 9.406735 8.00 Fold10
#> 97 0.9984190 0.9747928 9.406735 16.00 Fold10
#> 98 0.9976285 0.9617382 9.406735 32.00 Fold10
#> 99 0.9976285 0.9617382 9.406735 64.00 Fold10
#> 100 0.9968379 0.9483684 9.406735 128.00 Fold10
The average accuracy across ten folds is 99.79 with a standard deviation of 0.159.
| Method | KNN (k = 5) | LDA | QDA | Log. Regression | Random Forest (tuning param = ?) | SVM (tuning param = ?) |
|---|---|---|---|---|---|---|
| Accuracy | 99.81% | 98.28% | 99.46% | 99.56% | 99.96 | 99.79 |
| AUC | 99.99% | 98.93% | 99.82% | 99.91% | 99.37 | 99.97 |
| ROC | ||||||
| Threshold | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
| Sensitivity | 98.02% | 80% | 83.95% | 88.64% | 98.77 | 95.8 |
| Specificity | 99.87% | 98.89% | 99.98% | 99.92% | 100 | 99.92 |
| FDR | 3.87% | 29.57% | 0.87% | 2.71% | 0 | 2.51 |
| Precision | 96.13% | 70.43% | 99.13% | 97.29% | 100 | 97.49 |
(discussion on FHO data why we do this… what the benefits are… potential pitfalls)
(discussion somewhere about ROC curves AUC and… other metrics)
handling imbalanced classes
#| Method | KNN (k = `r k_knn`) | LDA | QDA | Log. Regression | Random Forest (tuning param = ?) | SVM (tuning param = ?)|
#|-------------------------:|:--------------:|:---------:|:---------:|:---------------:|:--------------------------------:|:---------------------:|
#| Accuracy | `r acc_knn_FHO`% | `r acc_lda_FHO`% | `r acc_qda_FHO`% | `r acc_LR_FHO`% | `r acc_RF_FHO` | `r acc_SVM_FHO` |
#| AUC | `r auc_knn_FHO`% | `r auc_lda_FHO`% | `r auc_qda_FHO`% | `r auc_LR_FHO`% | `r auc_RF_FHO` | `r auc_SVM_FHO` |
#| ROC | | | | | | |
#| Threshold | `r thresh_knn_FHO` | `r thresh_lda_FHO` | `r thresh_qda_FHO` | `r thresh_LR_FHO` | `r thresh_RF_FHO` |`r thresh_SVM_FHO` |
#| Sensitivity=Recall=Power | `r sens_knn_FHO`% | `r sens_lda_FHO`% | `r sens_qda_FHO`% | `r sens_LR_FHO`% |`r sens_RF_FHO` | `r sens_SVM_FHO` |
#| Specificity=1-FPR | `r spec_knn_FHO`% | `r spec_lda_FHO`% | `r spec_qda_FHO`% | `r spec_LR_FHO`% |`r spec_RF_FHO` |`r spec_SVM_FHO` |
#| FDR | `r FDR_knn_FHO`% | `r FDR_lda_FHO`% | `r FDR_qda_FHO`% | `r FDR_LR_FHO`% | `r FDR_RF_FHO` |`r FDR_SVM_FHO` |
#| Precision=PPV | `r prec_knn_FHO`% | `r prec_lda_FHO`% | `r prec_qda_FHO`% | `r prec_LR_FHO`% |`r prec_RF_FHO` | `r prec_SVM_FHO` |
#consider if I was able to find an additional data source like lidar or infrared to pair with this dataset to improve model performance... ?
| LDA | QDA | |
|---|---|---|
| Assumptions | this is a lot of text what happens when you put this much text in this table | |
| Tuning Parameters |